Let's say someone true polymorphs your snake familiar into a bandit and concentrates long enough to make it permanent, does the familiar stay a bandit when you dismiss them and resummon?
There are several ways that your familiar might get dismissed.
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons.
If you do this then it would keep any buff spells. This means it would continue to be a bandit.
Alternatively, you can dismiss it forever.
If you do this then you can get back a different familiar which would not have the buff spell. This means it would not be a bandit any more.
Note that, if your familiar drops to 0 hit points, true polymorph will go away:
The transformation lasts for the Duration, or until the target drops to 0 Hit Points or dies.
No, because a True Polymorphed familiar ceases to be a familiar.
True Polymorph states:
The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form.
A polymorphed creature is not the original creature. Compare it to Shapechange (the spell or the creature ability) or a druid's Wild Shape, that very specifically retains many of the abilities of the original creature.
For all intents and purposes, you put aside all mechanical aspects of the targeted creature and replace it with the mechanical aspects of the desired creature. This includes the adjustments made to the creature by the Find Familiar spell (like it's non-Beast type, required obedience, etc). The former familiar cannot be dismissed or recalled, because it is no longer a familiar.
The only thing that sticks around is the personality. Assuming it was well-treated, the familiar may still like its former master, but it is no longer bound to that master.
The description of Find Familiar states in part:
As an action, you can temporarily dismiss your familiar. It disappears into a pocket dimension where it awaits your summons. [...]
If you cast this spell while you already have a familiar, you instead cause it to adopt a new form. Choose one of the forms from the above list. Your familiar transforms into the chosen creature.
The combination of these two paragraphs says to me that the familiar is transported to a different place if you dismiss it but that its form is unaffected. You only get to change its form by recasting the spell.
Therefore, your Familiar would remain a bandit until you recast the spell and chose a new (or old) form for it.